15.69 Consider the two-way analysis of variance setup, with m observations per cell.

a. Show that the between-groups sum of squares can be written as follows:

SSG = Hm a K

i=1 x2i

~~ - HKmx2

b. Show that the between-blocks sum of squares can be written as follows:

SSB = Km a H

j=1 x2~

j~ - HKmx2

c. Show that the error sum of squares can be written as follows:

SSE = a K

i=1 a

H j=1 a

m l=1 x2 ijl - m a K

i=1 a

H j=1 x2 ij~

d. Show that the total sum of squares can be written as follows:

SST = a K

i=1 a

H j=1 a

m l=1 x2 ijl - HKmx2

e. Show that the interaction sum of squares can be written as follows:

SSI = ma K

i=1 a

H j=1 x2 ij~ - Hm a K

i=1 x2i

~~ - Km a H

j=1 x2~

j~ + HKmx2